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Equation 9 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

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in time that scales as poly(log⁡N,κ)\text{poly}(\log N, \kappa) , an exponential improvement in the matrix dimension N over the best classical algorithms available at the time, which scale roughly as Nκ\sqrt{\kappa} for a matrix with condition number κ\kappa [ 6 ] . What became known as the HHL algorithm is now routinely cited as the theoretical seed that later, explicitly labeled “quantum machine learning” proposals built their linear-algebra subroutines on top of.

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